In the art of speech processing, it is necessary to separate mixtures of multiple signals (including speech signals) from multiple sensors in a multipath environment. Such a separation of the mixtures without a priori knowledge of signals is known as blind source separation (BSS). BSS is very useful to separate signals that are from independent sources such as multiple speakers and sonar arrays. BSS techniques may be applied to speaker location tracking, speech recognition, speech coding, 3-D object-based audio signal processing, acoustic echo cancellers, channel equalization, estimation of direction of arrival, and detection of various biological signals such as EEG and MEG.
Most BSS techniques try to recover the original signals by nullifying the effect of multi-path effects. Although filters of infinite length are required for this purpose in general, filters of finite length also provide sufficient separation in most real world environments.
There are two popular approaches to this BSS problem: (i) multiple decorrelation (MD) methods that exploit the second order statistics of signals as independence measure and (ii) multichannel blind deconvolution (MBD) methods that exploit the higher order statistics.
The MD methods decorrelate mixed signals by diagonalizing second order statistics. [See, e.g. E. Weinstein, M. Feder, and A. V. Oppenheim, “Multi-channel signal separation by decorrelation,” IEEE Trans. Speech Audio Processing, vol. 1, no. 4, pp. 405-413, April 1993; Lucas Parra and Clay Spence, “Convolutive blind source separation of nonstationary sources”, IEEE IEEE Trans. Speech Audio Processing, pp. 320-327, May, 2000; D. W. E. Schobben and P. C. W. Sommen, “A frequency-domain blind signal separation method based on decorrelation,” IEEE Trans. Signal Processing, vol. 50, no. 8, pp. 1855-1865, August 2002; N. Murata and S. Ikeda, and A. Ziehe, “An approach to blind source separation based on temporal structure of speech signal,” Neurocomputing, vol. 41, no. 4, pp. 1-24, 2001] Diagonalization should be performed at multiple time instants for successful separation of signals. For this reason, these methods are only applied to nonstationary signals. These methods are quite fast and stable. The MBD methods, on the other hand, separate signals by minimizing mutual information of nonlinear-transformed separated signals which are transformed by a nonlinear function matched to statistical distributions of signals. [See, e.g. S. Amari, S. C. Douglas, A. Cichocki, H. H. Yang, “Novel on-line adaptive learning algorithm for blind deconvolution using the natural gradient approach”, Proc. IEEE 11th IFAC Symposium on System Identification, Japan, 1997, pp. 1057-1062; A. J. Bell and T. J. Sejnowski, “An information maximization approach to blind separation and blind deconvolution,” Neural Computation, 7, no. 6, pp. 1129-1159, November 1995; L. Zhang, A. Cichocki, and S. Amari, “Geometrical structures of FIR manifolds and their application to multichannel blind deconvolution,” Proc of Int. IEEE Workshop on Neural Networks and Signal Processing, pp. 303-312, Madison, Wis., USA, Aug. 23-25, 1999]